The Theory of the Jahn-Teller Effect

This book provides a comprehensive discussion of the Jahn-Teller Effect (JTE), focusing on the boson-fermion interaction. While current research is concerned with measuring and calculating ever more sophisticated and complex manifestations of the JT effect, the present volume takes away the epicycles of the theory and focuses on the symmetry dilemma at its core. When fermions and bosons meet, they get entangled and form a new dynamic reality. According to the rules of Molecular Symmetry, this reality is limited to a small set of patterns, with degeneracy cardinalities: 2, 3, 4, 5, and 6. The novelty of the book is that it adopts a unique mathematical technique, known as the Bargmann-Fock representation, and treats all degeneracies in detail. So far, this method was only applied to the simplest doublet case therefore its extension to the entire range of cases offers a new unified perspective. This volume will help the reader acquire a clear understanding of the JT effect, discover its universal mechanism and it will be a great tool for researchers and graduates working on this topic.

Presents all Jahn-Teller symmetry cases, with multiple diagrams and visualizations Provides a clear understanding of the mathematics of bosons and fermions Written by a leading figure in the Jahn-Teller community

Auteur

Arnout Ceulemans is Emeritus Professor of Theoretical Chemistry at the Catholic University of Leuven. His research is devoted to the development and application of group theory and topology to chemistry, with special focus on the study of the Jahn-Teller effect. He is the author of a textbook on 'Group Theory Applied to Chemistry', and co-authored 'Shattered Symmetry, Group Theory from the eightfold way to the periodic table'.

Contenu
Part I: BOSONS AND FERMIONS.- The Impossible Theorem.- Bosons and Fermions.- Boson-Fermion Interactions.- PART II: DYNAMIC SYMMETRIES.- The Rabi Hamiltonian.- The E x e Orbital Doublet.- The Spin Quartet 8 x (e + t2) System and the Symplectic Group Sp(4).- Ansatz for the Jahn-Teller Triplet Instability.- The Icosahedral Quartet and SO(9) SO(4) Symmetry Breaking.- SO(14) SO(5) Symmetry Breaking and the Jahn-Teller Quintet Instability.- Jahn's and Teller's Last Case: the Spinor Sextet.- PART III: TOPOGRAPHY.- Conical Intersections and Quantum Fields.- Topography and Chemical Reactivity.- Epilogue.- APPENDICES.- Appendix A The Displaced Oscillator.- Appendix B Derivation of the Coupling Coefficients.- Appendix C SU(n), SO(n), Sp(2n) Lie Algebras.- Appendix D The Birkhoff Transformation.- Appendix E Dirac's Monopole.- Appendix F Yang's Monopole.- Appendix G Topological Graph Theory.